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Simon chauveau
Simon chauveau

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From Analog to Digital: Signal Simulation

#matlab #github #simulation

Ever wondered how sound—like your voice or music—is transformed into digital data that can be stored on a computer or phone? In this post, we’ll explore how it works using a simple MATLAB simulation.

Simple simulation

Step 1 : Creation of Analog Signal
First, we create a sine wave (like a pure tone) at 100 Hz:

t = 0:0.0001:0.01;       % very fine step (continuous-like time)
f = 100;                 % frequency = 100 Hz
x_analog = sin(2*pi*f*t);
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Let’s visualize it:

figure;
plot(t, x_analog, 'LineWidth', 1.5);
title('Analog Signal (Sine Wave)');
xlabel('Time (s)'); ylabel('Amplitude');
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Analog Signal

This waveform represents our original sound.

Step 2 : Sampling the Signal
Sampling is like taking snapshots of the signal at regular intervals. The higher the sampling frequency, the better the quality.

I tested three sampling frequencies:

  • 150 Hz : Too slow
  • 200 Hz : Just enough (Nyquist rate)
  • 1000 Hz : Good

For this example, we use 1000 Hz:

Fs = 1000;               % Sampling frequency = 1 kHz
Ts = 1/Fs;               % Sampling period
n = 0:Ts:0.01;           % Discrete sample points
x_sampled = sin(2*pi*f*n);
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Visualizing the sampled signal:

figure;
stem(n, x_sampled, 'filled');
title('Sampled Signal');
xlabel('Time (s)'); ylabel('Amplitude');
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Signal Sample

Step 3 : Quantization
Quantization rounds each sample to the nearest level. More levels = better detail.

I tested:

  • 3 bits : 8 levels
  • 4 bits : 16 levels
  • 6 bits : 64 levels

Here’s the 4-bit version:

bits = 4;                           % Number of bits
levels = 2^bits;                    % Quantization levels
x_min = min(x_sampled);
x_max = max(x_sampled);
q_step = (x_max - x_min)/levels;    % Step size

x_index = round((x_sampled - x_min)/q_step); % Map samples to indices
x_quantized = x_index*q_step + x_min;        % Map back to amplitude
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Visualizing the quantized signal:

figure;
stem(n, x_quantized, 'filled');
title(['Quantized Signal (' num2str(bits) '-bit)']);
xlabel('Time (s)'); ylabel('Amplitude');
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Signal quantized

Step 4 : Encoding (Binary)
Now we convert each quantized value into binary:

binary_codes = dec2bin(x_index, bits); % Convert indices to binary words
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To display the first 10 samples:

disp('--- First 10 encoded samples ---');
disp(binary_codes(1:10));
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Step 5 : Digital Stream
Finally, we combine all binary codes into one bitstream:

bitstream = reshape(binary_codes.',1,[]); % Concatenate into one string
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Display the first 40 bits:

disp('--- First 40 bits of the stream ---');
disp(bitstream(1:40));
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Text Result

This bitstream is what computers and phones use to store and process sound.

GitHub

You can find the full MATLAB code and result images on my GitHub repository:

GitHub logo CSimon-278 / MathAlgo-Assinment1

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